What is the legal ruling regarding taking a false oath (yamin ghamus) upon the Book of Allah for my wife that I would not do such-and-such, then my wife absolved me and released me from this oath?

If a person swears by one of the names of Allah Almighty, or by one of His attributes, or by the Holy Qur'an, that he will not do something, this is a binding oath, and he must fulfill it.

If he breaks his oath and does what he swore to abandon, he must offer expiation for the oath. This expiation is: feeding ten poor persons, or clothing them, or emancipating a slave. If he cannot find any of these, then he must fast for three days.

This oath is not a false oath (yameen ghamus). A false oath is one that a person intentionally swears while lying, and it is considered a major sin.